Collective responses of bacteria to a local source of conflicting effectors

To cope in complex environments, motile bacteria have developed a chemosensory system that integrates multiple cues and directs their motion toward regions that it deems favorable. However, we have a limited understanding of the principles that govern bacterial behavior in complex stimuli fields. Here, we followed the spatial redistribution of E. coli cells in perplexing environments created by a local source of both beneficial (nutrients) and hazardous (low pH or indole) effectors. We identified two fundamentally distinct collective responses: a ‘trade-off’ response, in which bacteria sharply accumulated at a distance from the source that reflected a trade-off between the propagating effectors, and a ‘bet-hedging’ response, in which part of the bacteria accumulated away from the source, avoiding the hazardous effector, while the other part evaded the repulsive force and accumulated at the source. In addition, we demonstrate that cells lacking the Tsr sensor swim toward both repellents and, surprisingly, even toward pH values well below 7. Using a numerical analysis, we could correlate the collective bacterial responses with fundamentally distinct chemotactic force fields created along the channel by the propagation of the effectors and their unique perception by the chemosensory system.


Supplementary Text: Numerical analysis
To analyze the bacterial behavior in the channel we used where and being the dissociation constant of the ligand to the respective receptor in its or state, and ( , ) is the ligand concentration. We also introduced ℓ to allow using a dimensionless force Fche ( was set to 10 ), and thus, , the chemotaxis coefficient, has dimensions of velocity.
To integrate the advection-diffusion model numerically, we set Δ to be small enough to capture features seen in the experiments (usually set to Δ = 10 ), and set Δ dynamically as explained below. The simulations were initiated with n(x, t=0) = 0.1 (homogeneous distribution), and in each time step, we calculated the effector concentrations along the channel (generically assumed to be a 1D diffusion, see Fig. S1), calculated F ℎ . ( , ), and then numerically calculated the density flux as: where L is the length of the channel.
Chemical profiles are quasi-static for local chemotaxis. Because the effector distribution in the channel is dynamic, when a cell swims along the channel it experiences: Where is the swimming speed of the cell (~20 / ). The first term has been neglected in the simulations. This term can be evaluated as follows.
Since c(x, t) = f( / √4 ), the ratio between the two terms in Eq. 1 is To estimate this ratio, we plotted in the figure below the range-of-influence, ( ), of MeAsp as an upper limit for (symbols) and the expression 2 (line). Clearly, / 2 ≪ 1 for duration of most of the experiment.
A comparison between Rinf (symbols) and 2vt (line) at various times. The values of Rinf were taken from an experiment in which the source contained MeAsp (10mM). The value of 2vt was estimated assuming v = 20 μm/sec.

Nir Livne and Ady Vaknin
Correction of the cells' diffusion drift near the source. The channel was generically treated in the simulations as a 1D system. However, when cells accumulate at the source, e.g., in the presence of attractants, they tend to spread around the curved boundary of the source (Fig. S1). Since the curved boundary of the source is larger than the cross-section of the channel (its width), a band of cells that propagates towards the source is continuously expanding and thus, effectively diluted such that the cell density near the source is reduced (see Fig. S1A and related text). Moreover, since the effect is continuously enhanced as the cells approaches the source, this purely geometrical effect may modulate not just the bacterial-density at the source, but also the gradient of the bacterial density profile near the source and therefore, reduce the bacterial diffusive drift. We attempted to compensate for this effect by modifying the diffusion current very close to the source as follows: This correction did not affect the qualitative outcome of the simulations, but in cases where bacteria accumulate directly at the source, this correction led to somewhat better description of the bacterial distribution close to the source, as seen in the figure below.
Simulation outcomes with (red line) or without (green line) the correction accounting for the modified cell gradient near the source. Also shown are the corresponding measured profiles (blue symbols). Measurements were done with MeAsp (10mM) at the source.
(A) The diffusion profile in the channel. Fluorescein (10 µM) was added to the source and the florescence intensity along the channel was measured at various times, as labeled. Two sets of fits are shown, which mostly overlap: one, using a generic 1D constant-source diffusion: with D=0.56·10 -5 cm 2 /s (gray lines), and second, 2D simulations of the diffusion (blue lines) considering the semi-circular shape of the source demonstrated in the image below. Evidently, the shape of the source has a negligible effect on the diffusion at the relevant time scales. Also shown is an image exemplifying the bacterial accumulation, taken 1 hour after introducing a source of low-pH (4.5) and serine (1mM). The geometry of the channel and the source are also shown. The Notably, even at a short distance from the source the bacterial band is virtually perpendicular to the channel's axis. However, when cells accumulated directly at the source interface they spread over the curved source, and thus, lower the cell density near the source. To account for this reduction, we corrected the cell density very close to the source as follows: (B) Calibration of the fluorescence intensity with respect to bacterial cell density. Suspensions of GFP-expressing bacteria with different cell densities were prepared by serial dilution, injected into the channel, and the fluorescence intensity was measured. Evidently, the fluorescence intensity in the channel was linear with cell density.   (B) The pH profiles measured 1 and 3 hours after the source was introduced (as labeled) for experiments that were done in the absence (blue symbols) or presence (gray symbols) of non-fluorescent bacteria in the channel. The blue line marks the expected distribution should the pH expansion follow a generic diffusion pattern with D = 0.75·10 -5 cm 2 /sec (the value used for MeAsp). Note that in the presence of cells the pH near the source tends to be somewhat elevated. These profiles where measured by adding uniform distribution of Fluorescein along the channel (10 µM) and following its fluorescence intensity profile over time, which was independently calibrated against the pH in bulk samples.

Nir Livne and Ady Vaknin
Supplementary: Figure S4  Several lines of evidence demonstrated that setting the pH at the source to 4.5 did not have a significant effect on the bacterial physiology or directly distort the results (see also main text): (a) The bacterial accumulation generically observed with pH 4.5 and MeAsp at the source was similarly observed with pH 4.8 at the source (Fig. S4B). Note that pH 4.8 did not affect the chemotactic ability of the cells nor on their inherent fluorescence.
(b) The bacterial accumulation shifted away from the pH-4.5 source as the MeAsp concentration at the source was increased ( Fig. 2A, inset), indicating that the bacterial accumulation is not directly related to any harmful effect of the pH near the source.

Nir Livne and Ady Vaknin
(c) The distribution of Δ(tar tsr) cells along the channel, indicated by their fluorescence profile, was not affected by setting the pH source to 4.5 (Fig. 4A, inset). Moreover, not only the fluorescence profile, but also the number of cells per image along the channel was not affected (Fig. S4C, lower plot). Taken together, we can also conclude that the intrinsic fluorescence intensity of the cells was not significantly affected, even close to the source. Finally, the swimming speed of the bacteria was also not affected near the source (Fig. S4C, upper  plots).
(d) The bacterial accumulation created by combination of pH 4.5 and MeAsp (1 mM) at the source could be also observed by counting the number of cells per image along the channel, and was similar to that observed by recording the fluorescence profile (Fig. S4D, blue and grey symbols, respectively). Note, that the cell count at the peak is significantly underestimated owing to the difficulty of resolving single cells at the high cell density environment.
(e) Clearly, setting the pH at the source to 4.5 clearly did not prevent ΔTsr cells from approaching and accumulating at the source (Fig. 4A, red symbols). These cells were clearly swimming very close to the source.
For the indole force, we used the same parameters as detailed in Fig. S6 below. Dcells was set to 0.8•10 -5 cm 2 /sec in the case of the response to repellents alone (indole, pH) while it was set to 0.4•10 -5 cm 2 /sec in all other cases.  Left plots -The response of ΔTar cells to a low-pH source. In the experiment presented in the upper plot, the source pH was 4.5 while the bulk of the channel was set to 5.3. In the experiment presented in the lower plot, the source pH was 6 while the bulk of the channel was set to 7. Data is shown for 1 (light-blue symbols) and 3 (darker-blue symbols) hours. The outputs of the corresponding simulations are also shown (gray lines). Notably, to account for data, the value of α had to be approximately 10-fold higher at the lower pH range compared with the higher pH range (as labeled). The rest of the parameters were similar to those used in Fig. S5.